# Wild Cluster Bootstrapped p-Values For For Regression With Instrumental Variables This software estimates p-values using wild cluster bootstrapped t-statistics for instrumental variables regression models (Cameron, Gelbach, and Miller 2008). Residuals are repeatedly re-sampled by cluster to form a pseudo-dependent variable, a model is estimated for each re-sampled data set, and inference is based on the sampling distribution of the pivotal (t) statistic. Users may choose whether to impose the null hypothesis for independent variables; the null is never imposed for the intercept or any model that includes factor variables, interactions, or polynomials (although manually specified versions of these can circumvent the restriction). Confidence intervals are only reported when the null hypothesis is **not** imposed. ```r cluster.wild.ivreg( mod, dat, cluster, ci.level = 0.95, impose.null = TRUE, boot.reps = 1000, report = TRUE, prog.bar = TRUE, output.replicates = FALSE, seed = NULL ) ``` ## Arguments - `mod`: A linear (identity link) model estimated using `ivreg`. - `dat`: The data set used to estimate `mod`. - `cluster`: A formula of the clustering variable. - `ci.level`: What confidence level should CIs reflect? (Note: only reported when `impose.null == FALSE`). - `impose.null`: Should we impose the null Ho? - `boot.reps`: The number of bootstrap samples to draw. - `report`: Should a table of results be printed to the console? - `prog.bar`: Show a progress bar of the bootstrap (= TRUE) or not (= FALSE). - `output.replicates`: Should the cluster bootstrap coefficient replicates be output (= TRUE) or not (= FALSE)? Only available when impose.null = FALSE. - `seed`: Random number seed for replicability (default is NULL). ## Returns A list with the elements - **p.values**: A matrix of the estimated p-values. - **ci**: A matrix of confidence intervals (if null not imposed). ## Note Code to estimate clustered standard errors by Mahmood Arai: http://thetarzan.wordpress.com/2011/06/11/clustered-standard-errors-in-r/. Cluster SE degrees of freedom correction = (M/(M-1)) with M = the number of clusters. ## Examples ```r ## Not run: ############################################# # example one: predict cigarette consumption ############################################# require(AER) data("CigarettesSW", package = "AER") CigarettesSW$rprice <- with(CigarettesSW, price/cpi) CigarettesSW$rincome <- with(CigarettesSW, income/population/cpi) CigarettesSW$tdiff <- with(CigarettesSW, (taxs - tax)/cpi) fm <- ivreg(log(packs) ~ log(rprice) + log(rincome) | log(rincome) + tdiff + I(tax/cpi), data = CigarettesSW) # compute cluster-adjusted p-values cluster.wd.c <- cluster.wild.ivreg(fm, dat=CigarettesSW, cluster = ~state, report = T) ################################################ # example two: pooled IV analysis of employment ################################################ require(plm) require(AER) data(EmplUK) EmplUK$lag.wage <- lag(EmplUK$wage) emp.iv <- ivreg(emp ~ wage + log(capital+1) | output + lag.wage + log(capital+1), data = EmplUK) # compute cluster-adjusted p-values cluster.wd.e <- cluster.wild.ivreg(mod=emp.iv, dat=EmplUK, cluster = ~firm) ## End(Not run) ``` ## References Esarey, Justin, and Andrew Menger. 2017. "Practical and Effective Approaches to Dealing with Clustered Data." **Political Science Research and Methods** forthcoming: 1-35. . Cameron, A. Colin, Jonah B. Gelbach, and Douglas L. Miller. 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors." **The Review of Economics and Statistics** 90(3): 414-427. . ## Author(s) Justin Esarey

cluster.wild.ivreg function